Solve for $x$ : $6x^2 + 6x - 180 = 0$
Explanation: Dividing both sides by $6$ gives: $ x^2 + {1}x {-30} = 0 $ The coefficient on the $x$ term is $1$ and the constant term is $-30$ , so we need to find two numbers that add up to $1$ and multiply to $-30$ The two numbers $-5$ and $6$ satisfy both conditions: $ {-5} + {6} = {1} $ $ {-5} \times {6} = {-30} $ $(x {-5}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 6) = 0$ $x - 5 = 0$ or $x + 6 = 0$ Thus, $x = 5$ and $x = -6$ are the solutions.